In the years after RASS, a number of small- and medium-area X-ray surveys have been conducted based on XMM-Newton and Chandra [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}. Despite that the sky coverage of most of these surveys is smaller than 100 square degrees, hundreds of clusters have been detected, reaching fluxes of \(10^{-15}~{\rm erg}~{\rm s}^{-1}~{\rm cm}^{-2}\) , thanks to the high sensitivity of the instruments and the sufficient depth of the surveys. With well-understood selection functions and extensive follow-up observations, these samples play an important role in the study of cluster physics and the constraints of cosmology [11]}, [12]}, [13]}, [14]}, filling the gap between RASS and the next generation of X-ray all-sky survey. As the successor of ROSAT, one of the main design goals of eROSITA is to provide a larger X-ray selected sample of clusters. eROSITA is expected to detect \(\sim 10^5\)  clusters in the complete all-sky survey [15]}, [16]}, up to redshifts \(z\sim 1.5\) , down to masses of \(M_{500}\sim 10^{13}M_{\odot }\) , and reaching a flux limit of \(f_{0.5-2~{\rm keV}}\sim 10^{-14}~{\rm erg}~{\rm s}^{-1}~{\rm cm}^{-2}\) . This cluster catalog will inevitably be a valuable resource to test and constrain cosmological models, to trace the evolution of the large-scale structure, and to study cluster-related astrophysics.
